1913.] Sensations and the Theory of Forced Vibrations. 



495 



acted on by light increases, and we have, when dx/dt is zero or very small, 

 the condition of dark-adaptation, in which n reaches its maximum. 



In the dark-adapted eye we must regard the compound in which the forced 

 vibration is produced, as in a state of maximum concentration, and by all 

 the analogies of electro-chemical action, this must correspond with increased 

 resistance, or, in the mechanical model, with increased friction. 



In order therefore to obtain a graphic representation of the meaning of 

 dark-adaptation, we may compare together a series of curves of forced 

 vibrations with different values of the coefficient of friction. 



Let it be assumed that the quantity of the exciting substance set free 

 from the sensitive material may be taken as corresponding to the kinetic 

 energy of the forced vibration induced by the action of the light, the expres- 

 sion for which is 



B=-L-, where A=^£ = ^-P)p, 



p being the natural period of the resonator, n that of the impressed force, and 

 k representing friction.* 



The ratio p/n corresponds to the musical interval between the natural 

 period of the resonator and that of the forced vibration, and as the expres- 

 sion for A is symmetrical with regard to the ratio nfp it follows that if 

 values of B are taken as ordinates and ratios n/p as abscissae, we shall have 

 for each value of p a curve symmetrical about its apex. 



This consideration naturally suggests plotting the spectrum by what may 

 be called the " keyboard " system, in which, as in the piano, equal horizontal 

 distances correspond to equal musical intervals. Except in general illustra- 

 tion of the relation between ultra-violet and infra-red rays I do not think 

 this method has been used. It seems to offer certain advantages in dealino- 

 with problems of colour-sensation. 



Fig. 3 shows four hypothetical colour-sensation curves plotted on this 



A BC D bF GHK 



Fig. 3. 



Besonance Curves of the Colour Sensations Bed, Green, Blue, and Violet, with the 

 coefficient of friction, h = 0'2. For the dotted curve k — 0"1, but the ordinates are 

 reduced to one-quarter of their full value by the shunt factor. 



Barton, ' Handbook on Sound,' p. 145. 



